SOLUTION: Can someone be so kind as to tell me if I did these difficult homework questions correctly? 4. A fair coin is flipped 12 times and the sequence of heads and tails is observed.

Question 464687: Can someone be so kind as to tell me if I did these difficult homework questions correctly?
4.
A fair coin is flipped 12 times and the sequence of heads and tails is observed. Find the probability that the sequence consists of exactly 7 heads and 5 tails. Answer in fraction reduced to the lowest terms.
I said C(12,7)
5.
A fair coin is flipped 20 times and the sequence of heads and tails is observed. Find the probability that the sequence consists of AT LEAST two heads. Answer in fraction reduced to the lowest terms.
I said C(20,2)
6.
5 children are to be randomly chosen from a class of 7 boys and 8 girls. Find the probability that 2 boys and 3 girls are chosen. Answer in fraction reduced to the lowest terms.
I said C(7,2) x C(8,3)
7. An urn contains 20 numbered balls: 8 red, 7 white, and 5 blue. A sample of 9 balls is randomly chosen. Find the probability that the sample consists of 2 red, 3 white, and 4 blue balls. Answer in fraction reduced to the lowest terms.
C(8,2)x c(7,3) x C(5,4)
Are these right?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4.
A fair coin is flipped 12 times and the sequence of heads and tails is observed. Find the probability that the sequence consists of exactly 7 heads and 5 tails. Answer in fraction reduced to the lowest terms.
---
Binomial problem with n = 12 and p = 1/2
P(x = 5) = 12C5(1/2)^5*(1/2)^7 = 12C5(1/2)^12 = 792/4096 = 99/512
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5.
A fair coin is flipped 20 times and the sequence of heads and tails is observed. Find the probability that the sequence consists of AT LEAST two heads. Answer in fraction reduced to the lowest terms.
Binomial problem with n = 20 and p = 1/2
P(2<= x <=20) = 1 - P(0<= x <=1) = 1 - [1/2^20 + 20C2(1/2^20)]
= 1 - [(1+190)/2^20]
= 1 - (191/2^20)
---
== 1048385/1048576
========================

6.
5 children are to be randomly chosen from a class of 7 boys and 8 girls. Find the probability that 2 boys and 3 girls are chosen. Answer in fraction reduced to the lowest terms.
[C(7,2) x C(8,3)]/15C5 = 1176/3003 = 56/143
=====================================================

7. An urn contains 20 numbered balls: 8 red, 7 white, and 5 blue. A sample of 9 balls is randomly chosen. Find the probability that the sample consists of 2 red, 3 white, and 4 blue balls. Answer in fraction reduced to the lowest terms.
[C(8,2)x c(7,3) x C(5,4)]/20C9 = 4900/167950 = 245/8398
=================
Cheers,
Stan H.
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